A measurably evolving population (MEP) is an empirical concept that has grown out jointly from research on rapidly evolving populations (e.g., viral populations) and recent biotechnical developments. It is now possible for samples of short or moderately-sized molecular sequences to be obtained from populations that are separated sufficiently far apart in time, or for longer sequences to be obtained from samples that are separated by only a moderate number of generations, so that even with very low rates of mutation and substitution these serial samples will be genetically distinguishable. The proposed study anticipates the inevitable demand for new population genetic methods to analyze serial samples of sequences drawn from MEPs. In particular, we focus on the development of new coalescent- likelihood methods for estimating the intensity of historical population processes including migration, recombination, and growth, using serial samples. Our specific aims are: Incorporate and evaluate theoretical extensions of existing coalescent-likelihood methods, taking account of serial samples of molecular sequences, for the estimation of rates of genetic drift, growth, migration and recombination. Develop computer programs for the coalescent-likelihood estimation of the rates of genetic drift, growth, migration and recombination using sequences from serial samples, and make these programs freely available. Integrate a simple exponential model of change in effective population size into coalescent-likelihood estimators of migration and recombination rates, for the single-sample case. Develop a coalescent-likelihood method which uses serial samples to estimate piecewise exponential changes in effective population size.